KVELLER

Also a native speaker here, and I'm not quite sure of its context here!  

If I heard it outside of that context, I'd take it to basically mean "life always keeps going" or "life goes on".  

No idea what it means on the side of a cup to celebrate achievement in English!  Unless... could it be the school's motto?  Many schools have mottos, like little sayings.  In the UK, they're often in Latin.  For example, Cambridge University's is "Hinc lucem et pocula sacra" or "From here, light and sacred draughts".  

@Bauul I don't think the context really matters here. The school doesn't have a motto and other students got cups with other sentences in English, which are actually much more cliche, like "Today is going to be awesome".

They probably just found these cups with random messages and bought them as prizes :P

I've never heard this expression before.. Sounds like a goofed up mix of "Life goes on" and "what goes around comes around". I think your explanation is the most likely, maybe these particular cups were less expensive or something, lol